A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization is rather general and can be observed for arbitrarily small coupling strength in any model class. As a byproduct of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with $\delta$ pulses and a suitable phase response curve.

• Received 4 December 2014
• Revised 5 March 2015

DOI:https://doi.org/10.1103/PhysRevE.91.042916